18m^3*25n/5n^2*12m^2

To simplify the expression \( \frac{18m^3 \cdot 25n}{5n^2 \cdot 12m^2} \), we start by breaking it down step by step.

1. Multiply the numerators and denominators: The expression can be rewritten as: \[ \frac{18 \cdot 25 \cdot m^3 \cdot n}{5 \cdot n^2 \cdot 12 \cdot m^2} \]

2. Calculate the constants:

   • The numerator constants: \[ 18 \cdot 25 = 450 \]
   • The denominator constants: \[ 5 \cdot 12 = 60 \]

   Thus, we have: \[ \frac{450 \cdot m^3 \cdot n}{60 \cdot n^2 \cdot m^2} \]

3. Now simplify the constants: \[ \frac{450}{60} = 7.5 \]

4. Simplify the variables:

   • For \(m\): \[ m^{3-2} = m^{1} = m \]
   • For \(n\): \[ n^{1-2} = n^{-1} = \frac{1}{n} \]

5. Combine these results: So, the simplified expression becomes: \[ 7.5 \cdot m \cdot \frac{1}{n} = \frac{7.5m}{n} \]

Thus, the final simplified expression is: \[ \frac{7.5m}{n} \]